A) \[\frac{{{d}^{2}}u}{d{{x}^{2}}}=-2u\]
B) \[{{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)\]
C) \[{{\tan }^{-1}}\left( \frac{2x\sqrt{1-{{x}^{2}}}}{1-2{{x}^{2}}} \right)\]
D) zero
Correct Answer: C
Solution :
The general equations of alternating voltage and current in an AC circuit are as follows \[\frac{3}{2}=\frac{10+7n}{6+5n}\] ...(i) \[\Rightarrow \] ...(ii) Given that, \[\Rightarrow \] ...(iii) \[\therefore \] ...(iv) Comparing Eqs. (ii) and and (iv), we get, Peak value of current, \[I=\frac{E}{R'}\]Comparing Eqs. (i) and (iii), we get Peak value of voltage, £'0 = 100 V Now, r.m.s. value of voltage is given by \[E=-\frac{nd\phi }{dt},\] Similarly, i. m. s. value of current is given by \[I=-\frac{n}{R'},\frac{d\phi }{dt}\] Hence, reactance of the circuit is given by \[{{E}_{2}}-{{E}_{1}},\]
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